Fractions and Rational Numbers – What is the Difference?

Most of us go through years of school math courses and still are confused about some basic things. For example: Why can not you divide by zero? Why is .999 … equal to 1, and not a bit less?

There are loads of these kinds of questions, that would not be a cause of frustration at all, if they were taught reasonably and clearly.

Unfortunately most of these things are supposed to be covered in elementary school, and most elementary school teachers do not have a good understanding of basic math concepts. Instead they are supposedly to teach just a collection of "skills."

One of the simplest concepts that is usually left inadequately explained is the difference between fractions and rational numbers. Let's see if we can clear it up now.

A fraction is a number that expresses part of a whole as a quotient of integers (where the denominator is not zero).

A rational number is a number that can be expressed as a quotient of integers (where the denominator is not zero), or as a repeating or terminating decimal. Every fraction fits the first part of that definition. Therefore, every fraction is a rational number.

But even though every fraction is a rational number, not every rational number is a fraction.

Why? Consider this:

Every integer (all the whole numbers, including zero, and their negatives ….- 3, -2, -1, 0, 1, 2, 3 …) is a rational number , because it can be expressed as a quotient of integers, as in the case of 4 = 8/2 or 1 = 3/3 or -3 = 3 / -1 and so on. So integers such as 4 or 1 can be expressed as the quotient of integers.

But an integer is not a fraction . 4 is an integer, but it is not a fraction. 4 is not expressed as the quotient of integers. The difference here is in the wording.

A fraction is a number that expresses part of a whole. An integer does not express a part. It only expresses a whole number.

A rational number is a number that can be expressed as a quotient of integers, or as part of a whole, but fraction is a number that is (must be) expressed as a quotient of integers, or as part of a whole – there is a difference. The difference is subtle, but it is real.

There are slightly different variations of the definition of a fraction, including, "A fraction is the ratio of two whole numbers, or to put it simply, one whole number divided by another whole number."

That definition also shows that an integer is not a fraction, because an integer is not a ratio. It can be expressed as a ratio, but it is not a ratio in itself; it can be divided by another whole number, but it i s not being divided.

In a nutshell, the fractions are a subset of the rational numbers. The rational numbers contain the integers, and fragments do not.

Instant High Paying Jobs For Teens

So you have a teen on the hunt for a half decent job but what are their options these days. Everyone is telling them to baby sit or get a paper delivery job but both are time consuming and pay third world country rates when it comes to money in their pocket. It is even harder trying to land a job position that has been advertised somewhere as employers receive hundreds and hundreds of applications when advertising in the current job market.

A recent study shown that it is now taking the average person 4 – 7 months to find new employment and they expect that period of time to lengthen substantively over the next few years.

So what can I do you say, well thanks to modern technology all this is about to change. The days of searching endlessly for employment are fast coming to an end as the internet slowly takes over and starts filling this increasing need in the teen job market. When it comes to jobs for teens it is now possible for them to land their dream job in under ten minutes no matter who they are. When they take a job online there are no lengthy, intimidating interviews to go through and their application is always accepted no matter where you live or what qualifications they may or may not have. When you compare this to the difficulty of applying for and getting a normal advertised job it is no wonder that thousands of teens are switching to paid online jobs.

Paid online work beats traditional jobs hands down every time. Online jobs these days mostly consist of completing online survey's as these are generally higher paying when it comes to the types of work you can do online and they make fantastic jobs for teens. Most of these places are free to join and once they have signed up they can then start taking surveys and get very well paid for it. Most teens that are doing these surveys are at least $ 10 for a twelve minute survey with the money getting transferred to their account on completion.

The surveys themselves are extremely easy to complete and there is an unlimited number of different types of surveys that can be taken. There are no set times that they have to work, teens can quickly and easily work at their own pace as often or as little as they like each week, it's up to them. By just taking 3 surveys per day, 5 days per week, a teen is capable of earning $ 150.00 per week. Just try finding a job anywhere else that pay's as well as this that will hire them instantly.

Which survey companies they end up joining makes a huge difference to how much money they make. Pick the wrong ones and they could end up working for $ 2 – $ 5 per hour and getting very frustrated. Out of all the "Free To Join" paid survey sites online today there are only a small list of survey companies that have the genuine higher paying surveys available on a daily basis. Joining all of these top 7 companies ensures that they have and endless supply of high paying surveys to take every day when they log in.

So the choice is up to them, with the state of the current job market are they going to keep blogging.

The State Of Paralegal Employment In The United States

In 2004, Paralegal jobs and legal assistant’s jobs amounted to about 224,000 positions in all sectors of the economy of the United States. 84% of these had Paralegal qualifications above both Associate’s and Bachelor’s Degree, with about 10% Paralegals who had higher degrees leaving only about 6% Paralegals who have been trained on the job and working without formal Paralegal education.

As was in the beginning, private law firms controlled the lion share of employing about 70% of all working Paralegals then; today, according to present day employment statistics, this number has fallen as the Paralegal profession continues to expand into deferent fields of human endeavor. Many paralegals and legal assistants these days work for corporate legal departments and various levels of government agencies and None governmental organizations..

The U.S. Department of Justice is the largest employer of Paralegal within the Federal Government, followed by the Social Security Administration and the U.S. Department of the Treasury. State governments and Counties are also increasingly employing Paralegals to help make legal services available to the common man on the street.

More Paralegals are setting up private Paralegal offices in states where the law provides such privileges and work as freelance legal assistants, contracting their services to attorneys or corporate legal departments.

It is hoped that in the nearest future the Paralegal profession would be robust enough to receive country wide approval for Paralegals to practice freely providing legal assistance to all and sundry according to the law. This will be a step in the right direction considering that in the United Kingdom, Solicitors play the same roles as registered legal practitioners.

Choosing Ringbearer Gifts Does Not Have to Be A Bear

The significance of wedding rings is best illustrated in people's fear of losing them. There are people who boast of having never removed their wedding ring since their wedding day, though this is sometimes due to changes to their weight since they said, "I do." But really, how important are wedding rings? Moreover, how many times have we heard of what a nightmare it is to lose your ring? We hear stories of people losing their rings in the labyrinth of pipes underneath the kitchen sink. Then, there was the movie "American Wedding," in which wacky Steve Stiffler accidentally feeds the bride's wedding ring to a dog. Clearly, wedding rings are very important. Consequently, even though the ringbearer is one of the shortest members of the bridal party, his is the task of the tallest order. So, when you choose ringbearer gifts, keep in mind the critical role that your ringbearer plays.

The Ringbearer
The use of ringbearers is fairly modern. They tend to be young brothers or nephews of the bride or groom, and usually range in age from 5 to 10. In weddings that are formal, the ringbearer, or pageboy, has one of two different functions. First, the ringbearer might carry the bridal party's rings on a huge white satin pillow. Boys will be boys, and almost anything could happen during his waddle down the aisle. Usually, the best man himself secures the rings, or thread is used to attach the rings onto the ringbearer's pillow.

Another function of the ringbearer is to carry the bride's train, if it is lengthy.

The Basics
Whether the ringbearer totes the rings or holds the train, make him feel special through your choice of ringbearer gifts. For example, consider what your ringbearer likes. Here are some ringbearer gifts that might ring well with him.

Ring Bearer Fun Box Gift: This is decorated to look like a Ringbearer's tuxedo. Inside it is fun games, cookies, and candies.

Ringbearer Baseball Cap: This will remind the boy that he was in the starting lineup of the wedding ceremony.

Space Magic Cookie Pot: This is a bouquet that is packed with cookies and candies. What kid says no to sweets?

Ringbearer Activity Tote Bag: This is a fabric bag with several gift items inside.

Personalized Gifts
Aside from the obvious height difference, kids and adults are not too different from each other. Like adults, kids want to feel special, too. Personalized ringbearer gifts help you do just that. Here are a few personalized ringbearer gifts to consider.

Personalized Baseball: This will make any little leaguer feel like a big leaguer. The ball is mounted on a walnut-finish stand.

Ringbearer T-shirt: This will let your mini lord of the rings remember the special day. How could he not with his name is printed on the shirt?

Personalized Silver Plated Yo-Yo: Give a new twist to the old toy! Each time your ringbearer uses this ringbearer gift, he will remember his walk down the aisle.

Being the ringbearer in a wedding can be daunting for any youngster. Help your ringbearer enjoy the task by giving him a well-thought out ringbearer gift. Carefully chosen ringbearer gifts will make your wedding day one that will always ring a bell in your little ringbearer's mind.